Question: Simplify the following expression: $a = \dfrac{-32t^2 + 28t}{-4t^2}$ You can assume $t \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-32t^2 + 28t = - (2\cdot2\cdot2\cdot2\cdot2 \cdot t \cdot t) + (2\cdot2\cdot7 \cdot t)$ The denominator can be factored: $-4t^2 = - (2\cdot2 \cdot t \cdot t)$ The greatest common factor of all the terms is $4t$ Factoring out $4t$ gives us: $a = \dfrac{(4t)(-8t + 7)}{(4t)(-t)}$ Dividing both the numerator and denominator by $4t$ gives: $a = \dfrac{-8t + 7}{-t}$